Yes and no. Synthetic fabrics (minky, microfiber etc.) do not increase in absorbency over time, however, natural fabrics like bamboo, cotton and hemp will become more absorbent over the first 10 washes or so as the natural oils come out of the fabric. After this, multiple washings won’t increase the absorbency any further.
This is part of why it’s important to pre-wash your natural fabrics properly before use on baby.